As Nikita Khrushchev's ambassador in Budapest from 1953 to 1957, Mr. Andropov witnessed the uprising that toppled the Stalinist regime and the Soviet Army's installation of another whose loyalty to the Kremlin was unquestionable.

The new regime was headed by Janos Kadar, who subsequently managed to set Hungary on the moderate, reformist course it still follows.

Hungarians tend to see a link between Kadar's successful pragmatism and Andro-pov, who recently returned to the Soviet Secretariat as one of the two aides closest to Brezhnev.

They say Andropov had a lot to do with Brezhnev's eventual confidence in Kadar - who for many years has been the most effective leader in Eastern Europe.

''He realized what Kadar was setting out to do in 1956,'' a very senior Hungarian figure told this writer.

''You have to understand that Kadar was not greatly known at that time. Moreover, that he did not come to the leadership in favorable circumstances. (He disappeared midway through the uprising, then emerged at the head of the Soviet-sponsored government that most Hungarians received with disdain.)

''But it was Kadar who saw what was required - that a middle road was the only way. . . . And, remember, within a relatively very short time, Kadar began to win acceptance among the people.

''That is why we see Andropov today as - to use the popular term - a reformer and possibly also the next general secretary of the Soviet party.''

It was quite wrong, this source said, to see Andropov ''as a policeman'' (because of his 15 years as KGB chairman). ''You must keep in mind the fact that , when he took over, the KGB was very different from what it was in the Stalin years. His appointment was, in effect, very much a party one to bring the organization more under party control.''

At one time, Andropov was associated with Otto Kuusinen, an old Comintern figure of some importance in the de-Stalinization process of the Khrushchev years. Later, Andro-pov worked with Georgi Arbatov, longtime director of the Soviet USA Institute.

Following the passing of chief ideologist Mikhail Suslov early this year, Andropov returned to the Secretariat. According to those in the know here, he has not acquired all of Suslov's fields of competence (which in effect touched the whole Soviet scene) but did take over the more important ones.

Konstantin Chernenko, another possible Brezhnev successor, heads the Central Committee's general department. He and Andro-pov are regarded as more or less equally effective voices around the Soviet leader.

Andropov is concerned not only with ideology but also with foreign affairs. In addition to his ambassadorial term in Budapest, he had an advisory role over Czechoslovakia in 1968 (reportedly he was among those having reservations about intervention until the last moment) and has long handled Kremlin ties with all the ruling Communist parties.

The Hungarians profess to see indications of changes ahead in the Soviet Union. They speculate that some of the hints publicly dropped by Brezhnev recently might not have been made were Suslov still around. To that extent they read them as an indicator that Andropov and others think the time has come for quicker economic and social development inside the Soviet Union. The Hungarians, of course, would welcome this.

Recent conversations in Warsaw and Belgrade revealed that the Poles and the leaders of nonaligned Yugoslavia tend to see Andropov in a similar light.

Informed Poles seem convinced he is, at this juncture, Brezhnev's successor-designate. They view him as a party man first and foremost, and regard his rise in influence as a Brezhnev counterweight to the military.

A top-ranking Yugoslav party member credited Andropov with having already built ''considerable authority among the younger Russian intelligentsia as a 'liberal.' ''